Do you love limits?

Hey guys,i'm new here. Hope u can help me with those 3 problems:1)Let it be f,g:[-1,1]-> R; f,g - continous functions.Show that exist a,b ∈[-1,1],a<b so that f(a)=g(b) and f(b)=g(a) then there is c∈[-1,1],so that f(c)=g(c).My guess here it's Lagrange but i have no clue on how to apply it.2)Calculate lim n->inf ( 1/(2ln2)+1/(3ln3)+...+1/(nln(n)) )3)a,b,c > 0 so that a^x+b^x+c^x>=3, with any x∈R. Show that a*b*c=1Ty for help xD

Re: Do you love limits?

I think he might have meant 1/(2log2)+1/(3log3)+...+1/(nlogn).

For the first problem, did you mean f'(c)=g'(c)?

Last edited by anonimnystefy (2013-11-19 10:55:11)

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.

Re: Do you love limits?

it's 7e/16 i think.ok the thing is that i did this exercise 2 years ago but i lost the notebook and now i can't figure out how to solve it anymorei know that the sum is constant and i know it's something with xe/12 or xe/12 but i cannot remember exactly.

Re: Do you love limits?

The way the question is posed (with the limit instead of infinity as the upper sum limit), I would guess there is a missing term in front of the sum.

Hi bobbym

How fast does the sum converge?

Last edited by anonimnystefy (2013-11-20 06:38:17)

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.

Re: Do you love limits?

Yes that's a part i don't understand yet.I'm on last year of high school so i started learning about integrals just now.I still have to learn a bit more about integrals because at the time i solved it i used just Lagrange and derivates.I also found out how to solve 3) if you are interested but still no clue for 1).

Re: Do you love limits?

Not converge, sorry. What's its growth rate?

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.

Re: Do you love limits?

bobbym wrote:

Slower than 1 / n that is for sure.

I'm thinking it's O(log log n). Can you do the same limit, but with an 1/n in front of the sum.

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.

Re: Do you love limits?

Hi bobbym

anonimnystefy wrote:

bobbym wrote:

Slower than 1 / n that is for sure.

I'm thinking it's O(log log n). Can you do the same limit, but with an 1/n in front of the sum.

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.